A platformer is a game in which the primary novel interactive element is platforming. That is to say, the game engages the player by evolving and varying its platforming. Your first reaction to that ought to be "you used the word 'platforming' a whole lot of times in defining 'platformer'". That's because it's important to establish the game type beyond the play type. Many games contain platforming but are not platformers. Take for example Metroid or Contra. They're both full of jumping about, yet it's a constant; Metroid progresses via exploration and Contra through more threatening enemies.
|Few would argue that Sting is a platformer|
If you're not getting it, maybe you're a musical learner, or a kinesthetic. Try singing the last paragraph or shaking your monitor up and down, as it may suit your developmental disability. If you're a "by examples" learner, allow me to show you two games. One is a platformer and other is not. If you can, I recommend you go play these games to see exactly what I mean, because videos aren't the best control demos. On the left you have Gradius. Notice that in Gradius, when the player uses the control pad to move Vic Viper, it moves exactly in the direction you press, for the duration that you press it. Then it stops. No external forces are moving it, and navigation is not inherently a challenge. On the right is our old friend and loved one, Sonic the Hedgehog. Notice that Sonic falls from the sky, slides down hills, and generally does all kinds of stuff, even when the player drops the controller. Sonic is a platformer/hedgehog.
That ought to be enough to chew on for now, I'll be back later today or tomorrow with today's Ten Top Boppers.